Modelling And Forecasting Kenya’S Tea Export Prices Using Arima-Garch Model

CHAPTER 1: INTRODUCTION

Backround Study

Tea is a perennial crop grown for its leaves, which are processed to make tea for preparing beverages. Tea was first introduced in Kenya from India by a colonial settler G. W Caine in 1903 and is currently the leading export crop in Kenya. Some claim it is the most consumed beverage in Kenya. Tea is mainly grown in the Rift valley regions of Kenya such as Kericho, Nandi, Bomet, Kisii, Kakamega and some parts of the central regions of Kenya e. g. Nyeri. In these areas, the crop enjoys about 80 per cent favorable weather patterns. Tea is of great significance in Kenya’s economy as the largest industrial foreign exchange earner and an enormous resource for government via tax revenues. As per Kenya Tea Growers Association (KTGA), 2017, tea makes up 22 per cent of the value of exports, followed by cut flowers at 12 per cent and coffee at 43 per cent. Today, Kenya is the 3rd leading tea producer in the world accounting to 10% of the total world tea production(AFFA, 2015). In 2001, the tea industry turnover was US$ 474 Million accrued from export earnings with the balance being the value of the locally sold tea. The Kenya’s tea industry is also a key job creation and employment sector. According to KTGA, the Central Organizations of Trade Unions (COTU) has more than 100,000 members in the tea growing zones in the Rift Valley regions. The subsequent year, Kenya became second only to Sri Lanka in exports of black tea.

Generally, the success story of the Kenyan tea industry is a product of three main developments. First, the government policy after independence to incorporate small scale growers into the mainstream of the entire tea industry. Presently, the small scale growers under the umbrella of Kenya Tea Development Agency (KTDA) account for sixty per cent of the total tea production while the multinational sector together with the large scale growers account for the remaining forty per cent. The establishment of the efficient estate sector under the British Tea companies has also introduced revolutionary improvements in the estate and factory management with a resulting fivefold increase in output. The selection of high yielding varieties mainly by the Tea Research Foundation of Kenya (TRFK) plus the selection application of herbicides and improved planting and cultivation methods has also led to a dramatic positive effect on the yield. Although the tea industry has been completely liberalized, government control still exists under the Tea Board of Kenya (TBK). TBK is responsible for regulating tea trade and promotion in both local and international markets. Meanwhile, even though the Kenyan tea industry has been on the rise, several adverse forces presently threaten the tea industry. The main threat being the weak trend in the export prices of tea. This export price problem is as a consequence of the increase of the worldwide tea export which has occurred more rapidly than the world consumption. Over the past decade, there has been a consistent surplus of tea into the world market which has had an effect of depressing auction prices. The dollar price released for Kenya tea is at the same level as it was 10 years ago. There is a significant imbalance between the world supply and the tea demand.

Problem Statement

The core contributor to export success is favorable macro-economic policies and stable real exchange rate, which the government must pursue to keep export profitable and production efficient(Miano, 2009). According to (KNBS, 2017), tea exports in Kenya have been on the rise from 2012-2016 but are far from their real capacity. Decision making involves planning of uncertainty, finding the optimal level of production and even strategic planning for future expansion, based on past records using statistical models. Accurate short term forecast and prediction is therefore a very important key for the purposes of decision making. The government and other stakeholders require prior information on price trends for easy planning. Therefore it is important to forecast the export price of this commodity. In the recent past, there have been such instances of overestimation and/or underestimation of forecast prices. Evidence has accumulated showing that aggregated forecasts of sales by businessmen have had systematic errors. In periods of rising sales, business forecasts have tended to understate annual sales. In periods of falling sales, the forecasts have been too high. In other words, changes in sales have been typically underestimated. “When it costs a businessman something to make forecasting mistakes, he has reason to avoid them”(Carlson, 1967). It is against this backdrop that this study intends to employ the hybrid ARIMA- GARCH model to forecast prices which will aid the stakeholders of the tea industry in proper planning and evasion of unprecedented losses.

Objectives

General Objective

To model and forecast Kenya’s tea export prices using time series.

Specific Objectives

1. To specify the suitable ARIMA-GARCH model for forecasting.
2. To estimate the numerical values of the specified model.
3. To access and analyze the acceptability of the estimates obtained and test whether the statistical assumptions are fulfilled.
4. To analyze and examine the seasonal growth of Kenya’s tea exports.

Research Questions

• Is there a trend in the seasonal prices of tea exports?
• Is the data stationary?
• Is there any seasonal variation in the data?
• What is the best model to forecast these export prices?

Justification of the Study

The tea sector contributes largely to the external performance of the economy. This sector generates and saves foreign exchange for the country, by producing beverages which would otherwise have been imported. The generation of foreign exchange also contributes substantially to Kenya’s balance of trade and overall balance of payment. Accurate short term sunflower seeds forecasts were helpful to stakeholders in the sunflower industry. In order to make efficient plans of production, accurate price forecasts are needed. The ARIMA model can be employed in forecast of the US marketing year average price of sunflower seed. ARIMA model was used to forecast the season average sunflower seed price for the years 1991/92-1993/94.

The model forecasted monthly price for each year. When the forecast was compared to the average actual prices of farmers, the ARIMA forecasts were found to be extremely close to the actual prices. It is against this backdrop that the future performance of the sunflower industry may obtain information from ARIMA models to better their strategies of prediction/ forecast(Douvelis, 1994). It is nevertheless known that the ARIMA model has some shortcomings and in a bid to overcome this and improve the forecasting accuracy of the forecasts, this study will therefore employ the hybrid ARIMA-GARCH model to generate forecasts of Kenya tea export prices, which will be useful in ensuring continuous improvements are made in the tea sector to improve the quantity and price of tea exports.

Literature Review

In this chapter, studies related to quantity of exports, prices and real exchange rates are being reviewed. It also illustrates the use of statistical methods in analyzing the quantity of Kenya’s tea exports with their corresponding prices. This chapter is alienated under these sections:

• Trends in the quantity of exports and prices.
• Volatility Analysis.
• Hybrid ARIMA GARCH Model
• Studies related to Autoregressive Integrated Moving Average (ARIMA) model.
• Studies related to Generalized Autoregressive Conditional Heteroskedastic (GARCH) model.
• Studies related to comparison and Selection of the Best Forecasting Model
• Trends in the Quantity of Exports and Prices

Exports of agricultural products have played a key role to economic growth. However, structural adjustment programs of 1980’s interfered with the positive trend of foreign exchange earnings derived from these crops (Nzioki, 2005). It is a fact that the real exchange rate between different countries fluctuates over time. These fluctuations in relation to the quantities and prices of commodities in various countries have distinct impact on their economies and trade flows. At the firm and sectoral level, a positive effect of real depreciation has been found, but the effect at aggregate level has been found to be positive and negative in different countries (Colacelli, 2009). Structural adjustment programs aim at removal of overvalued exchange rates, abolition of subsidies, reduction of industrial protection and fiscal severity. These policies have a positive impact on terms of trade for the agricultural sector in favor of the tradable (Bainswagger, 1998). The growth rate under adjustment was found to be higher in sub-Saharan countries; which shows that African agriculture is responsive to changes in policies.

Volatility Analysis

In finance, volatility is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns. Real exchange rate is another crucial factor in the international market. It influences the global prices of agricultural commodities. Changes in exchange rate policy significantly produce an effect for a country’s domestic relative prices and economic growth (Oyejide, 1986). Therefore, a falling real exchange rate makes exportable goods less profitable. This leads to producers to divert their resources to other activities.

As a result, the export sector contracts and foreign exchange reduces. This leads to increased outflow of capital. The best way of studying how the government’s macro-economic decisions and policies affect agriculture is to evaluate the effects of such policies on the real exchange rates (Valdes, 1989). This stems from the fact that correct real exchange rate alignment is required if a country is to take advantage of the growth opportunities offered by international trade. Valdes defined real exchange rate as the ratio of tradable to price of non-tradable is determined by world market prices, nominal exchange rates and trade policies. Prices of non-tradable (home goods) are determined domestically, by changes in domestic supply and demand. Real exchange rate plays a major role in the profitability of tradable such as coffee and tea in agriculture. Therefore, real exchange rate is the perhaps the most influential price affecting incentive for agriculture.

Hybrid ARIMA GARCH Model

A time series is a set of numbers that measures the status of some activity over time. It is the historical record of a certain activity whereby the measurements are taken at equally spaced intervals with a consistency in the activity and the method of measurement. The core objective of time series modelling is to study the techniques and measures in drawing inferences from the past data. Several models can be employed to describe and analyze the sampled data and make appropriate forecasts for the future. The main advantage of these models is that they can handle any persistent pattern in the data (Abdullah & Tayfur, 2004). The field of finance, data for the macro economic variables are available at the most monthly, while in finance, one need to deal with a high frequency data e. g. hourly, daily or even in minutes. The structural models therefore seem not quite useful for out of sample forecasting. To avoid such problems, univariate or a theoretical model are often used to model and predict financial variables using information contained in past values and possibly current and past values of an error term.

One special class of time series models are ARIMA models which are often associated with Box and Jenkins (1976) for their efforts to systemize the entire methodology of estimating, checking and forecasting using ARIMA models (Mahesh, 2005). The Box-Jenkins method entails three key steps: the identification step, which implicates order determination of the AR and MA parts of ARMA model. The step involves statistical information such as the autocorrelation and partial autocorrelation (Box & Jenkins, 1976). The problem of estimating the order and the parameters of an ARIMA model remains an active area of research. Building good ARIMA models basically requires more experience than commonly used statistical methods such as regression(Rojasa et al. , 2008). In Box-Jenkins methodology, a non-stationary time series is made stationary by differencing the ARMA Model. In differencing, a new time series is built by taking differences of successive values eg xt-xt-1 along the non-stationary time series pattern. The ARIMA model is built by differencing the ARMA model where ‘I’ stands for Integrated.

The general accepted structure of ARIMA model is ARIMA(p, d, q) where p denotes the number of autoregressive parameters, d denotes the number of differencing passes and q denotes the number of moving average parameters (Ajoy & Dobrivoje, 2005). Despite the flexibility of the ARIMA model in forecasting a time series data, it is unable to handle volatility and non-linearity in time series data. Therefore, in a bid to handle volatility past studies have shown that Generalized Autoregressive Heteroskedastic (GARCH) models are used in commodity data series including exchange rates. Hence, combining the models aids in overcoming the shortcomings of each components model and thus improving the forecasting accuracy. The ARCH and GARCH models were developed by Engle (1982) and extended by Baillie (2002) and Nelson (1991). The first generation of GARCH models were unable to effectively handle volatility. This deficiency has been overcome by introduction of more flexible specifications which allow positive and negative shocks to have different impacts on volatility. These models include Exponential GARCH (EGARCH), the Glosten, Jagannathan and Runkle-GARCH (GJR-GARCH) and the Power GARCH (PGARCH) model (Chatayan & Songsak, 2010).

Studies related to Autoregressive Integrated Moving Average (ARIMA) model

In a study to compare the forecast capability of Box-Jenkins, Holt-Winters and stepwise regression model, it is established that each method has its own merits. For instance, the Box-Jenkins gives better forecasts in the short run but it requires time and expertise to execute. Further, for a time series data with less than 30 observations/data points, a combination of both Holt-Winter and stepwise regression is preferred. In cases of 50 and above observations, the Box-Jenkins is opted for. Finally, when the data has strong seasonal and long fluctuations, the Holt-Winters model is to be chosen (Newbold & Granger, 1974). The reason for post-sample forecasting accuracy of ARIMA models becoming worse than much simple time series methods is the way of making the series stationary in its mean. It is proposed that if alternative methods were implemented, ARMA models perform better than other methods used more frequently. Further, it is proved that using ARMA models to seasonally adjusted data improves post-sample accuracies and it simplifies use of ARMA models (Andersen & Weiss, 1984). In forecasting the market year average price of US sunflower seeds by ARIMA model for the years 1991/92-1993/94, the model forecasted the price of sunflower seeds of each month. It indicated that the forecast, weighted by the average estimated volume of the sales during each marketing month of the year calculated the seasons’ average price received by each farmer. The ARIMA forecast came very close to the actual price of the sunflower seeds during the marketing season (Douvelis, 1994).

Studies related to Generalized Autoregressive Conditional Heteroskedastic (GARCH) model

An attempt was made to investigate the changes in maize price levels and fluctuations in Ghana. A model to determine the wholesale price was reviewed where grain stocks were held for speculative storage and exports to neighboring countries in the Sahel. ARCH was applied to monthly maize data to test the model. Regression was applied in measuring changes in maize price volatility, and to conclude on the necessity of past prices, domestic and regional production, and commodity storage and trade in explaining the changes(Shively, 1996). In trying to analyze changes in monthly pig and pork price in 1991-1998, ARCH was applied. Empirical results of testing for unit-root were utilized in getting the stationarity of changes in pig and pork price, and a selected suitable lag through partial autocorrelation function (ShihMing, 1999). The future price basis of a commodity depends linearly on the conditional variance, significant coefficient, from seasonal data that is, from monthly as well as daily data are found if the conditional variance is modeled using GARCH model (Engle, Lilien, & Robins, 1987).

Studies related to comparison and Selection of the Best Forecasting Model (Sparks & Yurova, 2006) compared the performance of ARIMA and ARCH/GARCH on time series of daily equity prices for large companies. They found out that for one-step-ahead forecasts, ARCH/GARCH models outperform ARIMA models in modeling financial time series in terms of the most applied measure. ARIMA did not provide accurate point estimates and did not produce a relatively normal distribution of residuals. Therefore ARCH/GARCH is a better model than ARIMA for modeling financial time series data. (Pahlavani & Roshan, 2015) in their study to forecast exchange rate of Iran compared the performance of ARIMA and hybrid ARIMA-GARCH. The achieved results clearly showed that the best model ARIMA-EGARCH model, after the comparison of their forecasting performance. ARIMA-EGARCH model captured the volatility and leverage effect in the exchange rate returns and its forecast performance was more than the other models. (Al-Ajez, 2016) compared the performance of ARIMA and ARCH/GARCH models on time series of Traffic Accidents in Gaza Strip.

The study compared the forecasting capabilities of the GARCH model and the traditional ARIMA models. The best model for forecasting the Traffic Accidents was ARMA(1,1)-GARCH(1,1) which performed better than SARIMA(3,1,2)(1,0,1) because of its capability to captivate the time-varying conditional variances. ARMA(1,1)-GARCH(1,1) was a better model than SARIMA(3,1,2)(1,0,1) because the values for the statistical estimates MSE,RMSR,MAE and MAPE were smaller in this model than those computed using SARIMA(3,1,2)(1,0,1) model. There exist a similarity between GARCH model and ARIMA model except that higher order AR and MA model may often be approximated by a mixed ARMA model with fewer parameters using a rational polynomial approximation. Therefore, a GARCH can often be considered as an approximate to a higher order ARCH model. In describing changing variance for no obvious reason other than relative simplicity, GARCH(1,1) has become the standard model. In case the model is fitted to the data, it can be found that (α+β)- λ2. The main objective in the analysis of data transformation in Box-Cox (1964) technique is to estimate the parameter λ. For this reason, we will apply the maximum likelihood method to estimate data since it facilitates the calculations of likelihood function. It is also easy to obtain an approximate confidence interval for λ.